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Otras calculadoras
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- La ecuación:
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Ecuación x^4=(x-20)^2
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Ecuación 5-2*(x-1)=4-x
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Ecuación (x+6)^3=25*(x+6)
- Ecuación x+y+2=0
- Expresar {x} en función de y en la ecuación:
- 10*x-18*y=3
- 16*x+7*y=8
- -19*x+1*y=0
- -11*x-15*y=14
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Expresiones idénticas
- sinpi(dos x- cinco)/ dos =-sqrt2/2
- seno de número pi (2x menos 5) dividir por 2 es igual a menos raíz cuadrada de 2 dividir por 2
- seno de número pi (dos x menos cinco) dividir por dos es igual a menos raíz cuadrada de 2 dividir por 2
- sinpi(2x-5)/2=-√2/2
- sinpi2x-5/2=-sqrt2/2
- sinpi(2x-5) dividir por 2=-sqrt2 dividir por 2
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Expresiones semejantes
- sinpi(2x+5)/2=-sqrt2/2
- cos(x)*sin(x)+sqrt(2)/2*cos(x)-sqrt(2)/2*sin(x)-(1/2)=0
- sinpi(2x-5)/2=+sqrt2/2
- sqrt(2)*sin(2*x)*sin(x-pi/4)=2*(-sqrt(2)/2)
- cos*((pi*(2*x+6))/4)=-(sqrt2/2)
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Expresiones con funciones
- sinpi
- sinpi((x+11)/6)=-1/2
- sinpi(5*x+15)/6=1/2
sinpi(2x-5)/2=-sqrt2/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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sin(p)*I*(2*x - 5) -\/ 2
------------------ = -------
2 2
$$\frac{i \sin{\left(p \right)} \left(2 x - 5\right)}{2} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \sin{\left(p \right)} \left(2 x - 5\right)}{2} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(2 x - 5\right) \sin{\left(p \right)}}{2} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(2 x - 5\right)}{2} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \sin{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(2 x - 5\right)}{2} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(-5 + 2*x)/2)/w
Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(-5 + 2*x)
hacemos cambio inverso
$$\sin{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \sin{\left(p \right)} \left(2 x - 5\right)}{2} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(2 x - 5\right) \sin{\left(p \right)}}{2} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(2 x - 5\right)}{2} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \sin{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - -sqrt+2)/2 + i*w2*x/2+5/2 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 + sqrt(2)/2 + i*w*(-5 + 2*x)/2 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(2 x - 5\right)}{2} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(-5 + 2*x)/2)/w
w = 1 / ((sqrt(2)/2 + i*w*(-5 + 2*x)/2)/w)
Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(-5 + 2*x)
hacemos cambio inverso
$$\sin{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
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___ ___
5 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
x1 = - + ------------------------------------------------------- + -------------------------------------------------------
2 / 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$x_{1} = \frac{5}{2} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = 5/2 + sqrt(2)*i*sin(re(p))*cosh(im(p))/(2*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2)) + sqrt(2)*cos(re(p))*sinh(im(p))/(2*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2))
Suma y producto de raíces
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suma
___ ___
5 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
- + ------------------------------------------------------- + -------------------------------------------------------
2 / 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$\frac{5}{2} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
5 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
- + ------------------------------------------------------- + -------------------------------------------------------
2 / 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$\frac{5}{2} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
5 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
- + ------------------------------------------------------- + -------------------------------------------------------
2 / 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 2*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$\frac{5}{2} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ ___ \
I*\\/ 2 + 5*cos(re(p))*sinh(im(p))/ + 5*cosh(im(p))*sin(re(p))
---------------------------------------------------------------
2*(cosh(im(p))*sin(re(p)) + I*cos(re(p))*sinh(im(p)))
$$\frac{i \left(5 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2}\right) + 5 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)} + i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
(i*(sqrt(2) + 5*cos(re(p))*sinh(im(p))) + 5*cosh(im(p))*sin(re(p)))/(2*(cosh(im(p))*sin(re(p)) + i*cos(re(p))*sinh(im(p))))